Dynamic behaviour of direct spring loaded pressure relief valves in gas service: II reduced order modelling

Abstract

A previous study of gas-service direct-spring pressure relief valves connected to a tank via a straight pipe is continued by deriving a reduced-order model for predicting oscillatory instabilities such as valve flutter and chatter. The reduction process uses collocation to take into account a finite number N of acoustic pressure waves within the pipe, resulting in a set of 2N + 3 ordinary differential equations. Following a novel non-dimensionalization, it is shown analytically that the model can exhibit, at experimentally realistic parameter values, instabilities associated with coupling between the valve and acoustic waves in the pipe. The thresholds for each instability are such that for a given flow rate, the first mode to go unstable as the inlet pipe length increases is the quarter-wave mode, then a three-quarter wave, a 5/4-wave etc. Thus the primary mode of instability should always be due to the quarter wave. In the limit of low flow rates, a simple approximate expression is found for the quarter-wave instability threshold in the form of inlet pipe length against mass flow rate. This threshold curve is found to agree well with simulation of the full model. For higher flow rates there is a need to include fluid convection, inlet pressure loss and pipe friction in order to get good agreement. The reduced model enables the dependence of the stability curve on key dimensionless physical parameters to be readily computed.

Dynamic behaviour of direct spring loaded pressure relief valves: III valves in liquid service

“…This paper continues the previous work by the present authors in Hős et al (2014Hős et al ( , 2015 on practical considerations of mechanisms of instability in direct spring operated pressure relief valves (PRVs). Here we specifically consider valves in liquid, rather than gas, service.…”

“…Instead, in Hős et al (2015) we found an accurate stability criterion which we tested against experimental results for three different commercially available gas service PRVs. The key is to recognize that the fundamental instability causing valve flutter is a flow-induced Hopf bifurcation caused by an interplay between the valve natural dynamics and the fundamental quarterwave acoustic vibration mode in the pipe.…”

“…For a yet longer pipe, the limit-cycle flutter behavior will undergo a transition into large-amplitude chatter motion in which the valve impacts with its seat. Moreover, through reduced-order modelling, in Hős et al (2015) we were able to produce a close analytical approximation to this curve which depends only a few pipe and valve parameters. In addition, specific features of the valve geometry can cause static jumps, or fold bifurcations, but these do not necessarily lead to flutter and shall not be considered in the present work.…”

Classification of the bifurcation structure of a periodically driven gas bubble

“…This is a very common method to examine nonlinear systems in general, for details see e.g. [46][47][48][49]. The IVP solver was a 4th order Runge-Kutta scheme with 5th order embedded error estimation.…”

Effect of Disc Geometry on the Dynamic Stability of Direct Spring Operated Pressure Relief Valves

“…The corresponding industrial standard [1] and the literature [9] usually discusses stability as a function the driving mass flow rate and pipe length. This map can be seen in Figure 3(b).…”